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find all matchings in a graph

Given a graph $G$, is it possible to ask Sage to generate all possible matchings of $G$? I know that G.matching() gives a maximum matching of $G$ and I also know that Sage has an iterator which finds all perfect matchings of $G$.

If no command exists which asks Sage to give me all possible matchings of $G$, does anyone have an idea of how to write a program to ask Sage to do this?